Balanced forces are forces that are all present but add up to a resultant of zero. An absence of forces means none act at all. In both cases, the object keeps its velocity, so you cannot tell the two cases apart just from seeing constant motion.
This lesson closes the core sequence in forces and momentum. It depends on calculating a resultant force and on F = ma, because zero resultant force means zero acceleration.
Why is this idea often mixed up?
Everyday experience suggests that things slow down unless you keep pushing. That is because friction and air resistance act on them. Once those forces are in the diagram, the picture changes.
The rule to remember is: a resultant force changes velocity. Zero resultant force means unchanged velocity. An object at rest stays at rest. An object that is moving stays moving at the same speed in the same direction.
How do you decide which situation you have?
- Draw the force diagram as in drawing a force diagram.
- Add the forces with signs, as in the resultant-force lesson.
- Decide the resultant. If it is zero, forces are balanced. If it is not zero, the velocity is changing.
- Write the conclusion in terms of the resultant: “resultant force is zero, so the velocity is constant”.
Worked example
Invented situation: a student pushes a crate along a level floor at a steady speed. The push is 40 N forwards. The weight is 300 N. Explain whether the forces are balanced and find the friction.
Step 1, forces: push (forwards, 40 N), friction (backwards, unknown), weight (down, 300 N) and the normal force from the floor (up).
Step 2, vertical: the crate does not move up or down, so the normal force equals the weight: 300 N upwards. The resultant vertical force is zero.
Step 3, horizontal: steady speed means zero acceleration, so the resultant force is zero. Forwards is positive: 40 − friction = 0, so friction = 40 N backwards.
Step 4, conclusion: the forces are balanced. Forces are acting, but the resultant is zero, so the speed stays constant.
Check: 40 N forwards and 40 N backwards cancel. 300 N up and 300 N down cancel.
The mistake to watch for
A common slip is to say that a moving object must have a resultant force in its direction of motion.
Mistaken answer: “The crate is moving forwards, so the resultant force is forwards.”
The student linked motion with force instead of linking change in motion with force.
The correction is to write the question to yourself: “Is the velocity changing?” For a steady speed in a straight line, it is not. The resultant is zero even though the crate is moving.
A second slip is the opposite one: “no resultant force means no forces”. That also fails. The crate has four forces acting, and they cancel.
Check yourself
Try these, then open each answer.
1. A book lies on a table. Are there any forces on it? Is the resultant zero?
Show answer
Yes: weight acts downwards and the normal force from the table acts upwards. They are equal, so the resultant force is zero. Forces are present and balanced.
2. A spacecraft far from any planet drifts at steady speed in a straight line with its engines off. What can you say about the resultant force?
Show answer
The resultant force is zero. Here it is because essentially no force acts. The velocity does not change, so there is no acceleration.
3. A ball reaches its highest point after being thrown upwards. Its speed is instantly zero. Is the resultant force zero? Explain.
Show answer
No. The weight still acts downwards and nothing balances it (ignoring air resistance). The resultant is the weight, so the ball accelerates downwards even though its speed is zero at that instant.
Where this leads next
You can now read any motion statement in terms of resultant force. Test the full module with the forces and momentum practice set, and note the error types in a mistake log and retest queue so that you revisit them.
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